alleryStart learning →A grindstone starting from rest is given an angular acceleration of 14.7 rad/s^2 and turns through 1.00 rad. What is its final angular velocity?
A14.7 rad/s
B29.4 rad/s
C7.35 rad/s
D5.42 rad/s
Answer & Solution
Correct answer: D. 5.42 rad/s
1. Time is not given, so use omega squared = omega_0 squared + 2 alpha theta.
2. Starting from rest sets omega_0 = 0, leaving omega = square root of (2 alpha theta).
3. Substituting, omega squared = 2(14.7 rad/s^2)(1.00 rad) = 29.4 rad^2/s^2.
4. Taking the square root gives omega = 5.42 rad/s.
5. Answering 29.4 rad/s quotes omega squared and skips the square root.
6. Answering 14.7 rad/s quotes the angular acceleration, which has different units altogether.
_Source: OpenStax College Physics (CC BY 4.0), Ch 10 "Rotational Motion and Angular Momentum", section 10.4 Rotational Kinetic Energy: Work and Energy Revisited_
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